EXISTENCE AND UPPER HEMICONTINUITY OF EQUILIBRIUM DISTRIBUTIONS OF ANONYMOUS GAMES WITH DISCONTINUOUS PAYOFFS

This paper deals with large anonymous games with compact metric action spaces and payoff functions which are upper semicontinuous but not ne cessarily lower semicontinuous. Under the supremum norm topology on th e space of payoff functions and a tightness assumption on the game, th e existence of Nash equilibrium distributions and the closed graph pro perty of the equilibrium distribution correspondence are proved. rf th e space of payoff functions is given the hypotopology instead, then eq uilibrium distributions exist, but the equilibrium distribution corres pondence may not have a closed graph.